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Nope, you don’t have to. You can send them all an email message, which has a high probability of getting buried and not making it into your application folder – or you can just blow it off, which in truth has a low probability of affecting any of your admission results. You can probably think of other choices too. It’s a world of possibilities.
Then use your imagination. I don’t mean make up a lie, but think about how to present it in a less negative light. Brief, businesslike, and upbeat. To that end, I wouldn’t advise you to explain it the way you’ve explained it here (“my mom told me to write X, but she was wrong”). Sounds too much like you’re trying to avoid shouldering the blame for a mistake.</p>